Albert wants to show that tan(theta)sin(theta)+cos(theta)=sec(theta). He writes the following proof:tan(theta)sin(theta)+cos(theta)=sec(theta)sin(theta)/cos(theta) sin(theta)+cos(theta)=sec(theta)sin^2(theta)/cos(theta)+cos(theta)=sec(theta)What is the next step in this proof?A.) He should write tan(theta)=sin(theta)/cos(theta) to find a common denominator.B.) He should write cos(theta)=cos^2(theta)/cos(theta) to find a common denominator.C.) He should write cos(theta)=1-sin(theta) to convert all the terms to sine.D.) He should write sin(theta)=1-cos(theta) to convert all the terms to cosine.
Accepted Solution
A:
we have that tan(theta)sin(theta)+cos(theta)=sec(theta) [sin(theta)/cos(theta)] sin(theta)+cos(theta)=sec(theta) [sin²(theta)/cos(theta)]+cos(theta)=sec(theta)
the next step in this proof is write cos(theta)=cos²(theta)/cos(theta) to find a common denominator so
remember that sin²(theta)+cos²(theta)=1 {[sin²(theta)+cos²(theta)]/cos(theta)}------------> 1/cos(theta) and 1/cos(theta)=sec(theta)-------------> is ok
the answer is the option B.) He should write cos(theta)=cos^2(theta)/cos(theta) to find a common denominator.